9973是质数还是合数?PrimeSmash!——适合无聊时玩的消质数游戏

软件名称

PrimeSmash!

应用平台

  • iOS
  • MacOS
  • Android(可能)

推荐类型

【用户投递】

一句简介

Touch, Smash, and Remember prime numbers the fun way!
以有趣的方式点击、消除和记住质数!
(不知道怎么介绍,就把官方介绍的第一句话贴上去了)

应用简介

回到标题,9973是质数,所以应该点掉 :rofl:
估计没几个人会研究这种问题,所以这个游戏无聊的时候玩效果最好 :rofl:

我同学推荐给我的,当时记得我们一大群人围在一起玩这个游戏,然后争论一个数是不是质数
(至少比单纯的切水果更有意义一点 :rofl:
在几秒钟内就要判断一个数是不是质数,考验数学和运气
这个游戏整理了1-10000的所有质数,分为四个难度
如果遇到质数,就点击它,如果遇到合数,就切掉它,它会分解为随机两个因数,然后重复上述操作……就这么简单

官方介绍不贴了,太长了,又是全英文的

官方网站 && 应用商店地址

苹果 AppStore

Android……没找到

https://www.taptap.com/app/158963

这个游戏已经下架了,作者还有安装包吗?麻烦发一下

Perhaps the easiest way to see whether a number that is not very big is prime or not is by trial.

Suppose that n is a positive integer. n is not prime if and only if there are two integers s, t greater than one such that n = st. Without loss of generality, suppose that s \leq t. Hence s^2 \leq n, which is just s \leq \sqrt{n}. We have the following useful proposition:

Suppose that n is a positive integer. n is not prime if and only if there exists an integer not greater than \sqrt{n} which divides n.


Suppose that p is a prime number greater than three. It is not hard to verify that six cannot divide p or p - 2 or p - 3 or p - 4. Hence all prime numbers greater than three must be of the form 6k + 1 or 6k - 1, in which k is an integer.


Now let’s see whether N = 9\,973 is prime or not.

Clearly neither two or three divides N. \sqrt{N} is greater than 99 and less than 100. Hence it suffices to check whether there is a prime number which is less than 100 and divides N. There are exactly twenty-five prime numbers which is greater than one and less than a hundred:

2   3   5   7   11
13  17  19  23  29
31  37  41  43  47
53  59  61  67  71
73  79  83  89  97

None of the numbers above divides N:

2 | 9 973 - 1
3 | 9 973 - 1
5 | 9 973 - 3
7 | 98; 7 | 9 898; 9 973 - 9 898 = 75; 7 does not divide 75
11 | 9 900; 9 973 - 9 900 = 73; 11 does not divide 73
13 | 9 100; 9 973 - 9 100 = 873;
13 | 780; 873 - 780 = 93; 13 does not divide 93
17 | 10 200; 10 200 - 9 973 = 227;
17 | 170; 227 - 170 = 57; 17 does not divide 57
19 | 9 500; 9 973 - 9 500 = 473;
19 | 380; 473 - 380 = 97; 19 does not divide 97
23 | 9 200; 9 973 - 9 200 = 793;
23 | 690; 793 - 690 = 103; 23 does not divide 103
29 | 8 700; 9 973 - 8 700 = 1 273;
29 | 1 160; 1 273 - 1 160 = 113; 29 does not divide 113
31 | 9 300; 9 973 - 9 300 = 673;
31 | 620; 673 - 620 = 53; 31 does not divide 53
37 | 111; 111 | 9 990; 9 990 - 9 973 = 17; 37 does not divide 17
41 | 8 200; 9 973 - 8 200 = 1 773;
41 | 41^2 = 1 681; 1 773 - 1 681 = 92; 41 does not divide 92
43 | 8 600; 9 973 - 8 600 = 1 373;
43 | 860; 1 373 - 860 = 513;
43 | 430; 513 - 430 = 83; 43 does not divide 83
47 | 9 400; 9 973 - 9 400 = 573;
47 | 470; 573 - 470 = 103; 47 does not divide 103
53 | 10 600; 10 600 - 9 973 = 627;
53 | 530; 627 - 530 = 97; 53 does not divide 97
59 | 11 800; 11 800 - 9 973 = 1 827;
59 | 1 180; 1 827 - 1 180 = 647;
59 | 590; 647 - 590 = 57; 59 does not divide 57
61 | 12 200; 12 200 - 9 973 = 2 227;
61 | 2 440; 2 440 - 2 227 = 213; 61 does not divide 213
67 | 13 400; 12 200 - 9 973 = 3 427;
67 | 2 010; 3 427 - 2 010 = 1 417;
67 | 1 340; 1 417 - 1 340 = 77; 67 does not divide 77
71 | 7 100; 9 973 - 7 100 = 2 873;
71 | 2 130; 2 873 - 2 130 = 743;
71 | 710; 743 - 710 = 33; 71 does not divide 33
73 | 7 300; 9 973 - 7 300 = 2 673;
73 | 2 190; 2 673 - 2 190 = 483;
73 | 438; 483 - 438 = 45; 73 does not divide 45
79 | 7 900; 9 973 - 7 900 = 2 073;
79 | 2 370; 2 370 - 2 073 = 297; 79 does not divide 297
83 | 8 300; 9 973 - 8 300 = 1 673;
83 | 1 660; 1 673 - 1 660 = 13; 83 does not divide 13
89 | 8 900; 9 973 - 8 900 = 1 073;
89 | 890; 1 073 - 890 = 183; 89 does not divide 183
97 | 9 700; 9 973 - 9 700 = 273;
97 | 194; 273 - 194 = 79; 97 does not divide 79

Hence N must be prime.

正常玩法(不开挂)玩这个游戏容易消耗草稿纸(
所以为什么有人无聊时候会算这个wwwwww

那个晚上, 我没什么重要的事. 看到关于算学的东西, 我觉得自己多少能讲几句. 我就试着以我熟知的前二十五个高于一的素数判断九千九百七十三是否是素数.

原因零: 它是时间杀手.

原因一: 我刚好练习打字. 那个晚上, 我打开熟悉的马当编辑器, 双手在键盘上运动着. 曾经的练习是有回报的; 我不必盯着键盘即可输入符号与数字 (不使用小键盘区, 因为太远了, 影响我的效率). 打完字后, 我按 gg, 然后按了好几次 Ctrl + f, 然后又按了 gg, 按下 yG, 然后粘贴到文字区, 发送.

原因二: 想起了写书的时光. 去年, 我写了一本简单的代数书, 其亦讨论了素数的基础. 虽然书挺失败的, 但还是助我消磨无聊的时光.

总之, 这对我而言没什么坏处, 故我就打字地判断九千九百七十三是否是素数. 我希望我能更快地计算它. 我当然可以写一个小程序; 不过这可能会花更多时间, 因为我很久没写电脑程序了.

现在忙, 故我基本不会主动地逛论坛了. 每日有大量的碗要洗; 不过, 午饭跟晚饭可较舒适地在工作场所解决, 这也不坏.